Lexical Definition

‎κοσμοκράτωρ‎ kosmokrátōr (kos-mok-fat'-ore) world power ^G:N-M
from ‎κόσμος‎ and ‎κρατέω‎

ruler.

• a world-ruler, an epithet of Satan

Abbott-Smith

*† κοσμοκράτωρ, -ορος, ὁ (< κόσμος, κρατέω),
1. in Orphic hymns, al. (v. AR, Eph 6:12), a ruler of the whole world (and so in Rabbinic writings: קוֺזמוֺקְרָטוֺר).
2. a ruler of this world (in contrast to παντοκράτωρ): οἱ κ. τ. σκότους τούτου, the rulers of this dark world, Eph 6:12.†

Abbott-Smith References

Liddell-Scott-Jones

κοσμοκράτωρ-κράτωρ [ᾰ], ορος, ὁ,

lord of the world, epithet of οὐρανός, [Refs 5th c.AD+]

__2 of the Emperors, [Refs 2nd c.AD+]
__3 Astrology texts, ruler of the κόσμος, i.e. planet, [Refs 2nd c.AD+]; οἱ κ. τοῦ σκότους τούτου the cosmic rulers of this sinful world, [NT+4th c.AD+]

_{LSJ Scripture Refs: Eph.6.12}